12a
0105
(K12a
0105
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 9 4 7 12 1 6 10
Solving Sequence
4,7
8
9,12
10 1 3 2 6 11 5
c
7
c
8
c
9
c
12
c
3
c
1
c
6
c
11
c
5
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.55045 × 10
70
u
75
− 2.21319 × 10
69
u
74
+ ··· + 1.11366 × 10
71
b − 4.15501 × 10
71
,
1.74213 × 10
71
u
75
+ 4.23795 × 10
71
u
74
+ ··· + 2.22733 × 10
71
a + 2.49538 × 10
71
, u
76
+ 2u
75
+ ··· − 4u − 4i
I
u
2
= hu
2
+ b, u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 4u
2
+ a − 2u + 2, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
v
1
= ha, b + v + 2, v
2
+ 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 87 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h−1.55×10
70
u
75
−2.21×10
69
u
74
+· · ·+1.11×10
71
b−4.16×10
71
, 1.74×
10
71
u
75
+4.24×10
71
u
74
+· · ·+2.23×10
71
a+2.50×10
71
, u
76
+2u
75
+· · ·−4u−4i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
−0.782160u
75
− 1.90270u
74
+ ··· + 0.520711u − 1.12035
0.139220u
75
+ 0.0198730u
74
+ ··· + 6.72179u + 3.73093
a
10
=
−1.01250u
75
− 2.27723u
74
+ ··· − 4.68125u − 3.11714
−0.533374u
75
− 1.25764u
74
+ ··· − 10.8152u − 5.20956
a
1
=
−0.650123u
75
− 1.66160u
74
+ ··· + 1.45358u − 1.64453
−0.487576u
75
− 0.547614u
74
+ ··· − 12.0164u − 5.53730
a
3
=
u
u
3
+ u
a
2
=
−0.841202u
75
− 1.99701u
74
+ ··· − 1.61931u − 3.16059
−0.379305u
75
− 0.461175u
74
+ ··· − 15.6666u − 6.86635
a
6
=
u
4
+ u
2
+ 1
u
4
a
11
=
−0.866472u
75
− 2.19326u
74
+ ··· + 4.35819u + 0.256226
0.137653u
75
+ 0.177442u
74
+ ··· + 6.46899u + 3.72188
a
5
=
−0.389207u
75
− 1.15743u
74
+ ··· + 9.42404u + 2.44734
0.260915u
75
+ 0.504172u
74
+ ··· + 7.97047u + 4.09188
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.431038u
75
− 2.36353u
74
+ ··· + 19.7107u − 1.47053
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 44u
75
+ ··· + 64u + 1
c
2
, c
4
u
76
− 4u
75
+ ··· − 32u
2
+ 1
c
3
, c
7
u
76
+ 2u
75
+ ··· − 4u − 4
c
5
, c
11
u
76
+ 2u
75
+ ··· − 1536u − 512
c
6
, c
8
u
76
− 18u
75
+ ··· + 8u + 16
c
9
, c
10
, c
12
u
76
− 11u
75
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
− 20y
75
+ ··· − 2904y + 1
c
2
, c
4
y
76
− 44y
75
+ ··· − 64y + 1
c
3
, c
7
y
76
+ 18y
75
+ ··· − 8y + 16
c
5
, c
11
y
76
− 60y
75
+ ··· − 4980736y + 262144
c
6
, c
8
y
76
+ 78y
75
+ ··· − 25376y + 256
c
9
, c
10
, c
12
y
76
− 81y
75
+ ··· − y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455728 + 0.886899I
a = −0.439921 + 0.696332I
b = 1.31461 + 1.96237I
−3.01496 + 4.88820I 0
u = −0.455728 − 0.886899I
a = −0.439921 − 0.696332I
b = 1.31461 − 1.96237I
−3.01496 − 4.88820I 0
u = −0.242587 + 0.956338I
a = 0.126777 + 0.066932I
b = −0.636155 − 0.369316I
1.73376 + 2.76988I 0
u = −0.242587 − 0.956338I
a = 0.126777 − 0.066932I
b = −0.636155 + 0.369316I
1.73376 − 2.76988I 0
u = −0.300154 + 0.911723I
a = −0.298517 − 0.851449I
b = −0.312058 + 0.123815I
1.47131 + 2.48388I −3.97625 − 5.03156I
u = −0.300154 − 0.911723I
a = −0.298517 + 0.851449I
b = −0.312058 − 0.123815I
1.47131 − 2.48388I −3.97625 + 5.03156I
u = 0.966024 + 0.399968I
a = 1.59350 + 1.18770I
b = −0.081922 + 1.324250I
−8.41832 + 4.70970I 0
u = 0.966024 − 0.399968I
a = 1.59350 − 1.18770I
b = −0.081922 − 1.324250I
−8.41832 − 4.70970I 0
u = 0.329512 + 0.885353I
a = −0.405534 − 1.248930I
b = 0.298096 + 1.020110I
−9.33642 − 2.29589I −14.4533 + 3.3340I
u = 0.329512 − 0.885353I
a = −0.405534 + 1.248930I
b = 0.298096 − 1.020110I
−9.33642 + 2.29589I −14.4533 − 3.3340I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.014609 + 0.937770I
a = 0.077787 − 0.512771I
b = −0.534953 + 0.135567I
2.34039 + 1.36664I −1.16303 − 3.99068I
u = 0.014609 − 0.937770I
a = 0.077787 + 0.512771I
b = −0.534953 − 0.135567I
2.34039 − 1.36664I −1.16303 + 3.99068I
u = 0.459884 + 0.984169I
a = −0.470424 + 0.570630I
b = −0.096858 − 0.186331I
−0.26575 − 6.82949I 0
u = 0.459884 − 0.984169I
a = −0.470424 − 0.570630I
b = −0.096858 + 0.186331I
−0.26575 + 6.82949I 0
u = −0.892842 + 0.178693I
a = 1.49196 − 0.49172I
b = −0.184836 − 0.547448I
−7.03975 − 0.53268I −13.60013 − 1.07611I
u = −0.892842 − 0.178693I
a = 1.49196 + 0.49172I
b = −0.184836 + 0.547448I
−7.03975 + 0.53268I −13.60013 + 1.07611I
u = 0.370705 + 0.815640I
a = 0.885752 − 0.809176I
b = 1.140930 − 0.560496I
−1.92973 − 2.36042I −11.97570 + 5.12556I
u = 0.370705 − 0.815640I
a = 0.885752 + 0.809176I
b = 1.140930 + 0.560496I
−1.92973 + 2.36042I −11.97570 − 5.12556I
u = −0.687147 + 0.872513I
a = 0.607407 − 0.726512I
b = −0.268675 − 1.051890I
−1.20627 + 2.64433I 0
u = −0.687147 − 0.872513I
a = 0.607407 + 0.726512I
b = −0.268675 + 1.051890I
−1.20627 − 2.64433I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.819508 + 0.771659I
a = 0.959193 + 0.784255I
b = 0.071628 + 1.120740I
−4.98884 + 1.38431I 0
u = 0.819508 − 0.771659I
a = 0.959193 − 0.784255I
b = 0.071628 − 1.120740I
−4.98884 − 1.38431I 0
u = 0.737774 + 0.375248I
a = 0.700985 − 0.058139I
b = 0.393066 − 0.259197I
−2.29090 + 2.47958I −12.54782 − 6.36018I
u = 0.737774 − 0.375248I
a = 0.700985 + 0.058139I
b = 0.393066 + 0.259197I
−2.29090 − 2.47958I −12.54782 + 6.36018I
u = −0.412819 + 1.097580I
a = −0.185023 − 0.079467I
b = −0.39421 − 1.46601I
−3.92733 + 5.04411I 0
u = −0.412819 − 1.097580I
a = −0.185023 + 0.079467I
b = −0.39421 + 1.46601I
−3.92733 − 5.04411I 0
u = −0.084581 + 1.169710I
a = −1.176400 + 0.004565I
b = −0.763256 − 0.298095I
−1.90505 + 2.55692I 0
u = −0.084581 − 1.169710I
a = −1.176400 − 0.004565I
b = −0.763256 + 0.298095I
−1.90505 − 2.55692I 0
u = 0.839016 + 0.860281I
a = −0.041777 − 0.748609I
b = 0.134710 − 1.100950I
−5.55819 − 0.23440I 0
u = 0.839016 − 0.860281I
a = −0.041777 + 0.748609I
b = 0.134710 + 1.100950I
−5.55819 + 0.23440I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.271979 + 0.728849I
a = −0.158361 + 0.653747I
b = 1.02910 − 1.06917I
−1.19310 − 1.13454I −6.76169 + 0.12359I
u = 0.271979 − 0.728849I
a = −0.158361 − 0.653747I
b = 1.02910 + 1.06917I
−1.19310 + 1.13454I −6.76169 − 0.12359I
u = −0.868139 + 0.862907I
a = 0.59737 − 2.73241I
b = −1.22566 − 2.99061I
−16.9214 + 0.7018I 0
u = −0.868139 − 0.862907I
a = 0.59737 + 2.73241I
b = −1.22566 + 2.99061I
−16.9214 − 0.7018I 0
u = 0.922477 + 0.805175I
a = 0.94429 + 2.60615I
b = −0.84388 + 2.86674I
−12.94230 + 3.80906I 0
u = 0.922477 − 0.805175I
a = 0.94429 − 2.60615I
b = −0.84388 − 2.86674I
−12.94230 − 3.80906I 0
u = −0.836232 + 0.905395I
a = −2.05766 + 2.66021I
b = 0.29232 + 3.64643I
−7.63809 + 3.11486I 0
u = −0.836232 − 0.905395I
a = −2.05766 − 2.66021I
b = 0.29232 − 3.64643I
−7.63809 − 3.11486I 0
u = −0.857948 + 0.885149I
a = −1.26826 + 0.64516I
b = 0.000711 + 1.087770I
−9.36055 + 1.38432I 0
u = −0.857948 − 0.885149I
a = −1.26826 − 0.64516I
b = 0.000711 − 1.087770I
−9.36055 − 1.38432I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.756697 + 0.974249I
a = 0.514142 + 1.001570I
b = −0.369171 + 1.310900I
−4.36264 − 7.29337I 0
u = 0.756697 − 0.974249I
a = 0.514142 − 1.001570I
b = −0.369171 − 1.310900I
−4.36264 + 7.29337I 0
u = 0.538578 + 1.116610I
a = 0.302697 + 0.551457I
b = −0.38569 + 1.98073I
−5.90863 − 10.12690I 0
u = 0.538578 − 1.116610I
a = 0.302697 − 0.551457I
b = −0.38569 − 1.98073I
−5.90863 + 10.12690I 0
u = −0.592970 + 0.471852I
a = −3.20694 − 0.59745I
b = −0.29512 + 1.41882I
−4.34919 − 0.93999I −13.35028 − 0.85509I
u = −0.592970 − 0.471852I
a = −3.20694 + 0.59745I
b = −0.29512 − 1.41882I
−4.34919 + 0.93999I −13.35028 + 0.85509I
u = −0.912342 + 0.844662I
a = −0.218872 + 0.616385I
b = −0.077088 + 1.039100I
−9.29331 − 4.38669I 0
u = −0.912342 − 0.844662I
a = −0.218872 − 0.616385I
b = −0.077088 − 1.039100I
−9.29331 + 4.38669I 0
u = 0.814149 + 0.940313I
a = −0.976252 − 0.502401I
b = 0.142693 − 0.935816I
−5.30989 − 5.93397I 0
u = 0.814149 − 0.940313I
a = −0.976252 + 0.502401I
b = 0.142693 + 0.935816I
−5.30989 + 5.93397I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.890915 + 0.871947I
a = −2.50662 − 2.77031I
b = −0.08145 − 3.74380I
−11.54220 + 1.50989I 0
u = 0.890915 − 0.871947I
a = −2.50662 + 2.77031I
b = −0.08145 + 3.74380I
−11.54220 − 1.50989I 0
u = −0.839690 + 0.932663I
a = −0.114340 + 0.950490I
b = 0.136640 + 1.324130I
−9.21096 + 4.92275I 0
u = −0.839690 − 0.932663I
a = −0.114340 − 0.950490I
b = 0.136640 − 1.324130I
−9.21096 − 4.92275I 0
u = −0.028623 + 0.741045I
a = 0.901182 + 0.801845I
b = 1.242130 − 0.230928I
−0.778419 − 0.915356I −8.17479 + 0.79538I
u = −0.028623 − 0.741045I
a = 0.901182 − 0.801845I
b = 1.242130 + 0.230928I
−0.778419 + 0.915356I −8.17479 − 0.79538I
u = −0.831749 + 0.953826I
a = 2.62617 − 1.31938I
b = 0.75964 − 3.05829I
−16.6338 + 5.6115I 0
u = −0.831749 − 0.953826I
a = 2.62617 + 1.31938I
b = 0.75964 + 3.05829I
−16.6338 − 5.6115I 0
u = 0.851225 + 0.960515I
a = −1.84087 − 3.01630I
b = 0.48600 − 3.93886I
−11.25930 − 7.95455I 0
u = 0.851225 − 0.960515I
a = −1.84087 + 3.01630I
b = 0.48600 + 3.93886I
−11.25930 + 7.95455I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.979362 + 0.836980I
a = 1.13211 − 2.84930I
b = −0.64977 − 3.13939I
−16.4507 − 8.6893I 0
u = −0.979362 − 0.836980I
a = 1.13211 + 2.84930I
b = −0.64977 + 3.13939I
−16.4507 + 8.6893I 0
u = −0.845823 + 0.987552I
a = −0.790361 + 0.676405I
b = 0.305930 + 0.996362I
−8.83599 + 10.87580I 0
u = −0.845823 − 0.987552I
a = −0.790361 − 0.676405I
b = 0.305930 − 0.996362I
−8.83599 − 10.87580I 0
u = 0.830058 + 1.011970I
a = 2.23256 + 1.60407I
b = 0.47626 + 3.17393I
−12.2872 − 10.2704I 0
u = 0.830058 − 1.011970I
a = 2.23256 − 1.60407I
b = 0.47626 − 3.17393I
−12.2872 + 10.2704I 0
u = 0.355517 + 0.549560I
a = −0.85062 + 2.50656I
b = −0.533081 − 0.231328I
−2.83735 − 0.62709I −12.5628 + 8.5045I
u = 0.355517 − 0.549560I
a = −0.85062 − 2.50656I
b = −0.533081 + 0.231328I
−2.83735 + 0.62709I −12.5628 − 8.5045I
u = −0.868958 + 1.031790I
a = 2.28881 − 1.95912I
b = 0.45651 − 3.41131I
−15.8088 + 15.4587I 0
u = −0.868958 − 1.031790I
a = 2.28881 + 1.95912I
b = 0.45651 + 3.41131I
−15.8088 − 15.4587I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351693 + 0.492259I
a = −0.005897 + 0.641030I
b = −1.83569 + 0.69933I
−10.71290 − 0.53109I −14.2640 + 10.6415I
u = 0.351693 − 0.492259I
a = −0.005897 − 0.641030I
b = −1.83569 − 0.69933I
−10.71290 + 0.53109I −14.2640 − 10.6415I
u = −0.584306 + 0.050984I
a = 1.043370 − 0.004017I
b = 0.339589 − 0.133401I
−1.084430 − 0.034863I −8.53665 − 1.11512I
u = −0.584306 − 0.050984I
a = 1.043370 + 0.004017I
b = 0.339589 + 0.133401I
−1.084430 + 0.034863I −8.53665 + 1.11512I
u = 0.368819
a = −10.6583
b = −0.443242
−3.00667 −66.4610
u = −0.365463
a = 1.13150
b = 0.541163
−0.844711 −11.8210
12
II.
I
u
2
= hu
2
+b, u
8
−2u
7
+· · ·+ a + 2, u
9
−u
8
+2u
7
−u
6
+3u
5
−u
4
+2u
3
+u +1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
−u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 4u
2
+ 2u − 2
−u
2
a
10
=
−u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 3u
2
+ 2u − 1
0
a
1
=
−u
2
− 1
−u
2
a
3
=
u
u
3
+ u
a
2
=
−u
6
− u
4
− 2u
2
− 1
−u
8
− 2u
6
− 2u
4
− 2u
2
a
6
=
u
4
+ u
2
+ 1
u
4
a
11
=
−u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 4u
2
+ 2u − 2
−u
2
a
5
=
u
4
+ u
2
+ 1
u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
8
+ 4u
6
− 3u
5
+ 10u
4
− u
3
+ 7u
2
− 6u − 8
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
4
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
, c
11
u
9
c
6
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
9
, c
10
(u − 1)
9
c
12
(u + 1)
9
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
4
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
7
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
5
, c
11
y
9
c
6
, c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
9
, c
10
, c
12
(y −1)
9
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = 0.919539 − 0.026486I
b = 0.915114 + 0.271383I
0.13850 + 2.09337I −5.80108 − 4.26451I
u = −0.140343 − 0.966856I
a = 0.919539 + 0.026486I
b = 0.915114 − 0.271383I
0.13850 − 2.09337I −5.80108 + 4.26451I
u = −0.628449 + 0.875112I
a = −0.353872 + 0.283586I
b = 0.370873 + 1.099930I
−2.26187 + 2.45442I −11.99086 − 2.54651I
u = −0.628449 − 0.875112I
a = −0.353872 − 0.283586I
b = 0.370873 − 1.099930I
−2.26187 − 2.45442I −11.99086 + 2.54651I
u = 0.796005 + 0.733148I
a = −1.166200 − 0.316186I
b = −0.096118 − 1.167180I
−6.01628 + 1.33617I −17.3564 − 0.5967I
u = 0.796005 − 0.733148I
a = −1.166200 + 0.316186I
b = −0.096118 + 1.167180I
−6.01628 − 1.33617I −17.3564 + 0.5967I
u = 0.728966 + 0.986295I
a = −0.363527 − 0.802398I
b = 0.44139 − 1.43795I
−5.24306 − 7.08493I −15.8155 + 4.8919I
u = 0.728966 − 0.986295I
a = −0.363527 + 0.802398I
b = 0.44139 + 1.43795I
−5.24306 + 7.08493I −15.8155 − 4.8919I
u = −0.512358
a = −5.07188
b = −0.262511
−2.84338 −2.07210
16
III. I
v
1
= ha, b + v + 2, v
2
+ 3v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
9
=
1
0
a
12
=
0
−v − 2
a
10
=
1
v + 3
a
1
=
v + 2
v + 3
a
3
=
v
0
a
2
=
2v + 2
v + 3
a
6
=
1
0
a
11
=
−v − 2
−v − 2
a
5
=
−v − 2
−v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −11
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
6
, c
7
c
8
u
2
c
4
(u + 1)
2
c
5
, c
9
, c
10
u
2
+ u − 1
c
11
, c
12
u
2
− u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
6
, c
7
c
8
y
2
c
5
, c
9
, c
10
c
11
, c
12
y
2
− 3y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.381966
a = 0
b = −1.61803
−10.5276 −11.0000
v = −2.61803
a = 0
b = 0.618034
−2.63189 −11.0000
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
76
+ 44u
75
+ ··· + 64u + 1)
c
2
(u − 1)
2
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
76
− 4u
75
+ ··· − 32u
2
+ 1)
c
3
u
2
(u
9
+ u
8
+ ··· + u − 1)(u
76
+ 2u
75
+ ··· − 4u − 4)
c
4
(u + 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
76
− 4u
75
+ ··· − 32u
2
+ 1)
c
5
u
9
(u
2
+ u − 1)(u
76
+ 2u
75
+ ··· − 1536u − 512)
c
6
u
2
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
76
− 18u
75
+ ··· + 8u + 16)
c
7
u
2
(u
9
− u
8
+ ··· + u + 1)(u
76
+ 2u
75
+ ··· − 4u − 4)
c
8
u
2
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
76
− 18u
75
+ ··· + 8u + 16)
c
9
, c
10
((u − 1)
9
)(u
2
+ u − 1)(u
76
− 11u
75
+ ··· + 3u + 1)
c
11
u
9
(u
2
− u − 1)(u
76
+ 2u
75
+ ··· − 1536u − 512)
c
12
((u + 1)
9
)(u
2
− u − 1)(u
76
− 11u
75
+ ··· + 3u + 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
76
− 20y
75
+ ··· − 2904y + 1)
c
2
, c
4
(y − 1)
2
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
76
− 44y
75
+ ··· − 64y + 1)
c
3
, c
7
y
2
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
76
+ 18y
75
+ ··· − 8y + 16)
c
5
, c
11
y
9
(y
2
− 3y + 1)(y
76
− 60y
75
+ ··· − 4980736y + 262144)
c
6
, c
8
y
2
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
76
+ 78y
75
+ ··· − 25376y + 256)
c
9
, c
10
, c
12
((y − 1)
9
)(y
2
− 3y + 1)(y
76
− 81y
75
+ ··· − y + 1)
22
